Positioning systems such as the U.S. Department of Defense Global Positioning System (GPS), and the Russian GLObal'naya Navigatsionnay Sputnikovaya Sistema (GLONASS), are increasingly used in a variety of applications, both civilian and military. In such systems, one or more receivers or similar apparatus are used to interpret received signals to determine, among other things, the current position of the one or more receivers and whoever or whatever is carrying it/them.
Unfortunately, positioning systems are not immune to attempts to subvert the system by spoofing, i.e. presenting fake signals to a positioning system receiver in order to induce it to accept, as valid, false position, velocity and/or timing information. Typically, the intent of spoofing is to deflect, surreptitiously, a dynamic platform (sometimes hereinafter “victim”) from its intended course to some other course at the discretion of the spoofing agent (sometimes hereinafter “spoofer”). The term “navigation signals” will sometimes be used herein to describe signals broadcast by a navigation system in a form for, and for the purpose of, providing at least one receiver such as a radio navigation receiver with information useful for determining the location of an antenna or antenna element of the receiver.
Let {right arrow over (a)} be the vector characterizing the location (xa, ya, za) of the antenna, or antenna element, a, component of a radio navigation receiver. Let {right arrow over (u)}m be the unit line of sight (LOS) vector from a to the radio transmitter, rm, of a radio navigation signal, nm. The location, {right arrow over (r)}m, of each rm is known either because it is stored in a database or because it is transmitted by with the navigation signal or some combination of both.
Let the scalar, Φm be a measurement of the value of the signal nm, as observed at a. The value of the signal is a quantization of the navigation information carried by the signal, the information might be range, pseudo-range, phase or timing information; all of which can effectively be scaled into the basic spatial units of the coordinate frame x, y, z. The contribution of this measurement, Φm, to the navigation estimate of the location of a is characterized by equation {right arrow over (a)}={right arrow over (r)}m−Φm{right arrow over (u)}m. This equation reduces to Φm=∥{right arrow over (r)}m−{right arrow over (a)}∥ (Equation 1). If the measurement is phase then it will contain an unknown number of whole cycles plus a part cycle i.e. Φm=2πI+Φm where I is an integer. An adequate set of measurements from n transmitters enables resolution of the location of a.
The spoofer substitutes misleading or spoofing signals, sm, for some, or all, of the legitimate navigation signals, nm, with the objective of corrupting the navigation system's estimate of position in such a fashion that the corruption is not detected by the navigation system.
It is assumed that the navigation system has some estimate, {right arrow over (â)}, of its location and can thus form an a priori estimate of Φm=∥{right arrow over (r)}m−{right arrow over (a)}∥. In order for the misleading measurement, Φm, generated by the spoofer to be believable the following condition must be true, |{circumflex over (Φ)}−m−Φ|<∂m (Equation 2), where ∂m is a threshold which takes into account the statistics of the possible error in the a priori estimate {circumflex over (Φ)}m and the statistics of the measurement noise and the desired level of certainty in the veracity of the measurement. In addition to passing the threshold condition of Equation 2 there is another hurdle for the spoofer to overcome. The set of measurements of Equation 1 from n transmitters must be self-consistent. Let {circumflex over (Φ)}+m be the post facto estimate (after the navigation solution incorporating Φm has been formed). In order for the set of n measurements to be deemed self-consistent the following condition must be met, Σm=1n({circumflex over (Φ)}+m−Φm)2<Δn2 (Equation 3), where the threshold, Δn2, is calculated in a similar statistical fashion to the threshold in Equation 2. By accurately tracking the vehicle being spoofed, by carefully simulating the navigation signals, and by controlling the rate at which the misleading information diverges from the true information to ensure compliance with the conditions of Equation 2 and Equation 3, a spoofer may succeed even if all the spoofing signals are broadcast from a single location. The tests of Equations 2 and 3 above, or similar procedures, are applied as standard practice to test measurements incorporated in a navigation solution in order to avoid incorporating faulty measurements.
As the possibility of a spoofer succeeding exists using previously known methods and apparatus, there is a need for methods and apparatus for preventing spoofing of positioning system receivers, in particular satellite positioning system receivers such as GPS and GLONASS receivers.
Additional information on positioning systems and the techniques they use can be obtained by reference to at least the following publications, each of which is incorporated in its entirety by reference herein:    (1) Global Positioning System: Signals, Measurements and Performance, Pratap Misra, et al., ISBN: 0970954409.    (2) GPS Bluebook, The Institute of Navigation    (3) Monographs of the Global Positioning System (“GPS Red Books”), The Institute of Navigation.    (4) Institute of Navigation Proceedings of the National Technical Meeting 2003, Precise Velocity Estimation Using a Stand-Alone GPS Receiver, F. van Graas, A. Soloviev, NTM 03.    (5) U.S. Pat. No. 5,583,774, Assured-Integrity Monitored-Extrapolation Navigation Apparatus, Dec. 10, 1996.    (6) U.S. Pat. No. 6,417,802, Integrated Inertial/GPS Navigation System, Jul. 9, 2002.